Course notes for Math 234

Alec's course notes for Math 234

• Overview and prerequisites for multivariable calculus (essentially chapter 12)
• Notes on Curves (Chapter 13)
• Notes on Surfaces (Chapter 14 sections 1–6)
• Notes on applications of multivariable differential calculus (Chapter 14 sections 7–10)
• Notes on multivariable integral calculus (Chapter 15)
• Notes on work integrals and potentials (Chapter 16 sections 16.1–3)
• Notes on Green's theorem for loop integrals in the plane (§16.4)
• Notes on Surface integrals (§§16.5-6)
• Notes on Gauss's theorem and Stokes' theorem (§§16.7-8)

• Physical applications of Gauss's and Stokes' theorem

  Angenent      Thomas   topic
  ============  ======   ======================================
  ch 1 sec 1-4  14.1     functions of several variables
  ch 1 sec 5    14.2     continuity and limits
  ch 2 sec 1-2  14.3     partial derivatives
  ch 2 sec 3-4  14.4     chain rule
  ch 2 sec 5    14.5     directional derivatives and chain rule
  ch 3 sec 4    14.7     extreme values and saddle points
  ch 3 sec 12   14.8     lagrange multipliers
  ch 4 sec 2    15.1     double integrals
  ch 4 sec 2.8  15.3     polar coordinates